Compact capture and protected bridges on the Koras–Russell cylinder
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Abstract
On an adapted model of the Koras-Russell cylinder, we give explicit compression of a closed C-star carrier and a sufficient criterion for ambient compact capture: the planar polynomial hull of the scalar image under q = xy+1 must avoid 1. This yields fixed Runge capture domains, including the connected inverse image of the plane slit along [1,infinity). Joint capture can be corrected to approximate the identity on a globally holomorphically convex parametrized ball inside a fixed Runge Euclidean domain. Prescribed compact bridges of positive thickness can thus be captured while protecting the ball without scalar-range separation. A complementary convex-ball argument treats certain protected bodies through q=1, and an analytic disk explains the obstruction to extending weighted contraction to the entire punctured chart. These are qualitative capture criteria.
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Research details
- Subjects
- Mathematics · Complex Analysis · Geometry
- Keywords
- Complex Analysis, Geometry, mathematical research
- Manuscript date
- 2026-10-24
- Reader reuse
- No additional permission granted
Scope
Explicit KR-cylinder carrier; sufficient scalar-hull/fixed-cut capture; protected prescribed bridges within these domains; separate joint-convex q=1 ball protection.
Disclosures
AI-assisted tools supported research exploration, literature review, manuscript preparation and internal verification. The author retains responsibility for the work.
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